Pub Date : 2024-03-26DOI: 10.1088/1361-6404/ad37e3
J. Etxebarria
Conditionally convergent series are infinite series whose result depends on the order of the sum. One of the most famous examples of conditionally convergent series of interest in Physics is the calculation of Madelung's constant α in ionic crystals. The appearance of this type of series is quite disturbing to students and often causes misunderstandings. In this work we analyze the physical meaning of the conditional convergence from a pedagogical point of view. The problem is posed using a toy model of ionic crystal in which the lattice sums can be calculated explicitly for various forms of expansion of the crystal about a central core. It is seen directly how the Coulomb series does not converge to α when there are charge accumulations on the surfaces. Therefore, it becomes clear what the appropriate strategy should be when choosing the order of summation to arrive at the correct value of α.
{"title":"Physical meaning of conditionally convergent series: the calculation of the Madelung constant","authors":"J. Etxebarria","doi":"10.1088/1361-6404/ad37e3","DOIUrl":"https://doi.org/10.1088/1361-6404/ad37e3","url":null,"abstract":"\u0000 Conditionally convergent series are infinite series whose result depends on the order of the sum. One of the most famous examples of conditionally convergent series of interest in Physics is the calculation of Madelung's constant α in ionic crystals. The appearance of this type of series is quite disturbing to students and often causes misunderstandings. In this work we analyze the physical meaning of the conditional convergence from a pedagogical point of view. The problem is posed using a toy model of ionic crystal in which the lattice sums can be calculated explicitly for various forms of expansion of the crystal about a central core. It is seen directly how the Coulomb series does not converge to α when there are charge accumulations on the surfaces. Therefore, it becomes clear what the appropriate strategy should be when choosing the order of summation to arrive at the correct value of α.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-26DOI: 10.1088/1361-6404/ad37e4
Heinz-Juergen Benno Schmidt, Thomas Broecker
We investigate the question discussed in the literature as to whether the magnetic field can perform work using two models that describe interacting magnetic dipoles. In the first model, the dipoles are realized by rigidly rotating charge clouds, whereas in the second model, one of the two dipoles is described by a real macroscopic spin density. The theoretical foundations of the second model are formulated in a recently published paper. We derive equations of motion and detailed energy balance for both models when the initial magnetic moments are parallel to the connecting line of the initial dipole positions. In this scenario the ``large" dipole remains stationary and generates external magnetic field in which the ``small" dipole is accelerated. The answer to the title question depends on the choice of criteria for ``work of the magnetic field".
{"title":"The magnetic field does not perform work - or does it?","authors":"Heinz-Juergen Benno Schmidt, Thomas Broecker","doi":"10.1088/1361-6404/ad37e4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad37e4","url":null,"abstract":"\u0000 We investigate the question discussed in the literature as to whether the magnetic field can perform work using two models that describe interacting magnetic dipoles. In the first model, the dipoles are realized by rigidly rotating charge clouds, whereas in the second model, one of the two dipoles is described by a real macroscopic spin density. The theoretical foundations of the second model are formulated in a recently published paper. We derive equations of motion and detailed energy balance for both models when the initial magnetic moments are parallel to the connecting line of the initial dipole positions. In this scenario the ``large\" dipole remains stationary and generates external magnetic field in which the ``small\" dipole is accelerated. The answer to the title question depends on the choice of criteria for ``work of the magnetic field\".","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2cf6
Orion Ciftja, Cleo L Bentley Jr
The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.
{"title":"Electrostatic potential of a uniformly charged annulus","authors":"Orion Ciftja, Cleo L Bentley Jr","doi":"10.1088/1361-6404/ad2cf6","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2cf6","url":null,"abstract":"The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2ec1
Luiz G M Ramos, Antonio S de Castro
The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.
{"title":"Revisiting the bound states of a confined delta potential","authors":"Luiz G M Ramos, Antonio S de Castro","doi":"10.1088/1361-6404/ad2ec1","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2ec1","url":null,"abstract":"The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2b98
Chaelee Dalton, Brian Farlow, Warren M Christensen
Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.
{"title":"Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application","authors":"Chaelee Dalton, Brian Farlow, Warren M Christensen","doi":"10.1088/1361-6404/ad2b98","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2b98","url":null,"abstract":"Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-14DOI: 10.1088/1361-6404/ad2cf5
Rod Cross
An inverted pendulum can be stabilised by hand or by a high frequency sinusoidal vertical oscillation of the bottom end or by feedback control if a horizontal force is applied at the bottom end. The pendulum is unstable if a sinusoidal force is applied in a horizontal direction at the bottom end. It is shown in the present paper that an inverted pendulum can be stabilised if a low frequency horizontal force is applied at the bottom end to right the pendulum after it falls through a small angle. The technique requires a measurement of the fall angle but is not sensitive to the actual fall angle. The technique represents a simple example of feedback control and is more easily understood than vertical oscillation of the bottom end.
{"title":"A horizontally driven inverted pendulum","authors":"Rod Cross","doi":"10.1088/1361-6404/ad2cf5","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2cf5","url":null,"abstract":"An inverted pendulum can be stabilised by hand or by a high frequency sinusoidal vertical oscillation of the bottom end or by feedback control if a horizontal force is applied at the bottom end. The pendulum is unstable if a sinusoidal force is applied in a horizontal direction at the bottom end. It is shown in the present paper that an inverted pendulum can be stabilised if a low frequency horizontal force is applied at the bottom end to right the pendulum after it falls through a small angle. The technique requires a measurement of the fall angle but is not sensitive to the actual fall angle. The technique represents a simple example of feedback control and is more easily understood than vertical oscillation of the bottom end.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-13DOI: 10.1088/1361-6404/ad336d
Zahid García Córdova, Dana Sofia Limón, Jesus Alejandro Torres
An affordable optical project for students is explained in this work. The experiment only requires a handheld laser illuminating a structure with stationary vibrations induced, but the interpretation of this phenomenon demands a strong understanding of optical interference and modal behavior of a bar. The operating principle employs the speckle phenomenon, which is a type of interference between coherent light incident on a rough surface and its reflection. This interference occurs in a luminous plane outside of the vibrating object and shows a granular structure due to the brightness fluctuations. Speckle is static but if the surface illuminated oscillates, the plane of interference moves from one side to the other, causing a streak pattern. Mode shapes of the object under examination can be naked eye detected from streak patterns. What is more, this phenomenon can be photographed using a manual focus digital camera. Therefore all the components of the procedure can be available (or acquired) by almost any physics laboratory, at any level, which would be unthinkable for optical experiments just a few years ago.
{"title":"Speckle interference for naked-eye detection of vibrations","authors":"Zahid García Córdova, Dana Sofia Limón, Jesus Alejandro Torres","doi":"10.1088/1361-6404/ad336d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad336d","url":null,"abstract":"\u0000 An affordable optical project for students is explained in this work. The experiment only requires a handheld laser illuminating a structure with stationary vibrations induced, but the interpretation of this phenomenon demands a strong understanding of optical interference and modal behavior of a bar. The operating principle employs the speckle phenomenon, which is a type of interference between coherent light incident on a rough surface and its reflection. This interference occurs in a luminous plane outside of the vibrating object and shows a granular structure due to the brightness fluctuations. Speckle is static but if the surface illuminated oscillates, the plane of interference moves from one side to the other, causing a streak pattern. Mode shapes of the object under examination can be naked eye detected from streak patterns. What is more, this phenomenon can be photographed using a manual focus digital camera. Therefore all the components of the procedure can be available (or acquired) by almost any physics laboratory, at any level, which would be unthinkable for optical experiments just a few years ago.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140394412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-12DOI: 10.1088/1361-6404/ad2c2d
Rod Cross
Calculations are presented on the trajectory of a golf ball that rolls across the inclined surface of a golf green. The ball follows a curved path and comes to a stop at a point displaced at an angle to the initial launch direction. It is shown that the displaced angle is independent of the launch speed but depends on the launch angle and the ratio of the incline angle to the coefficient of rolling friction. The stopping distance is proportional to the launch speed squared. A simple experiment is described to check the calculations.
{"title":"Trajectory of a golf ball on a sloping green","authors":"Rod Cross","doi":"10.1088/1361-6404/ad2c2d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2d","url":null,"abstract":"Calculations are presented on the trajectory of a golf ball that rolls across the inclined surface of a golf green. The ball follows a curved path and comes to a stop at a point displaced at an angle to the initial launch direction. It is shown that the displaced angle is independent of the launch speed but depends on the launch angle and the ratio of the incline angle to the coefficient of rolling friction. The stopping distance is proportional to the launch speed squared. A simple experiment is described to check the calculations.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-12DOI: 10.1088/1361-6404/ad2c2f
Spyros Efthimiades
The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.
{"title":"Derivation of the Schrödinger equation from QED","authors":"Spyros Efthimiades","doi":"10.1088/1361-6404/ad2c2f","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2f","url":null,"abstract":"The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-12DOI: 10.1088/1361-6404/ad2c2e
Milan Batista
This short paper presents a simple analytical model for the abrupt termination of circular motion, as discussed in the ‘The Most Mind-Blowing Aspect of Circular Motion’. The model confirms that when a string is released, a ball at the far end of the string continues to move in a near-circular motion for a short time.
{"title":"The initial trajectory of a ball released from uniform circular motion","authors":"Milan Batista","doi":"10.1088/1361-6404/ad2c2e","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2c2e","url":null,"abstract":"This short paper presents a simple analytical model for the abrupt termination of circular motion, as discussed in the ‘<italic toggle=\"yes\">The Most Mind-Blowing Aspect of Circular Motion’</italic>. The model confirms that when a string is released, a ball at the far end of the string continues to move in a near-circular motion for a short time.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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